76.10.16 problem 16

Internal problem ID [17538]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 3. Systems of two first order equations. Section 3.6 (A brief introduction to nonlinear systems). Problems at page 195
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 10:40:03 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-\left (x \left (t \right )-y \left (t \right )\right ) \left (1-x \left (t \right )-y \left (t \right )\right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right ) \left (2+y \left (t \right )\right ) \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=-(x(t)-y(t))*(1-x(t)-y(t)),diff(y(t),t)=x(t)*(2+y(t))],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],t]==-(x[t]-y[t])*(1-x[t]-y[t]),D[y[t],t]==x[t]*(2+y[t])},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved